1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SashulF [63]
2 years ago
10

Heya!

Mathematics
2 answers:
dimulka [17.4K]2 years ago
6 0

Answer:

the answer is in last picture

ArbitrLikvidat [17]2 years ago
4 0

Answer:

See Below.

Step-by-step explanation:

We are given that PQRS is a square. A, B, C, and D are the points of the sides PQ, QR, RS, and SP, respectively.

And we are given that AQ = BR = CS = DP.

This is shown in the figure below.

And we want to prove that ABCD is a square.

Since PQRS is a square, it follows that:

m\angle P=m\angle Q=m\angle R=m\angle S=90^\circ

Likewise:

PQ=QR=RS=SP

PQ is the sum of the segments PA and AQ:

PQ=PA+AQ

Likewise, QR is the sum of the segments QB and BR:

QR=QB+BR

Since AQ = BR and PQ = QR:

PA+AQ=QB+AQ

Therefore:

PA=QB

Likewise, RS is the sum of the segments RC and CS:

RS=RC+CS

Since RS = PQ and CS = AQ:

RC+CS=PA+CS

Thus:

RC=PA=QB

Repeating this procedure for the remaining side, we acquire that:

PA=QB=RC=SD

And since each of the angles ∠P, ∠Q, ∠R, and ∠S is 90°, by the SAS Theorem, we acquire:

\Delta AQB\cong\Delta BRC\cong \Delta CSD\cong \Delta DPA

Then by CPCTC, we acquire:

AB=BC=CD=DA

However, this means that ABCD could be either a rhombus or a square, so we need to prove that the angles are right angles.

The interior angles of a triangle always sum to 180°. Since they are right triangles, the two other angles must equal 90°. Thus, for ΔAQB:

m\angle QAB+m\angle QBA=90^\circ

By CPCTC, ∠PAD≅∠QBA. Thus:

m\angle QAB+m\angle PAD=90^\circ

∠DAB forms a linear pair. Therefore:

m\angle PAD+m\angle QAB+m\angle DAB=180

By substitution and simplification:

m\angle DAB=90^\circ

So, ∠DAB is a right angle.

By repeating this procedure, we can establish that ∠ABC, ∠BCD, and ∠CDA are all right angles. This is not necessary, however. Since we concluded that AB = BC = CD = DA, and that we have one right angle, then ABCD must be a square.

You might be interested in
What is 5au + 24av - 5bu - 30bv​
Blizzard [7]

Answer:

59

Step-by-step explanation:

5au+24av-5bu-30bv

rearrange it

5au+5bu-24av-30bv

similar letter cross each other

5a+5b-24a-30b

rearrange it

5a+24a-5b-30b

similar letter cross each other

5+24-5-30

29- -30=59

-and - = +

5 0
2 years ago
4k – 3 = -2k + 3 help me please lol
hoa [83]

Answer: k=1

Step-by-step explanation:

4k-3=-2k+3

take -3 and 3 and add them up on one side and change the sign

4k=-2k+3

           +3

4k=-2k+6

take the -2k and change the sign and add to 4k

4k=6

2k

6k=6

now divide both sides with x

6k/6= 6/6

k= 1

6 0
3 years ago
Read 2 more answers
What is 8/12 + A/12=2/b
il63 [147K]

Answer:

the answer i got was a=−8b+24/b

Step-by-step explanation:

hoped I helped:)

8 0
3 years ago
A vehicle purchased for $20700 depreciates at a constant rate of 5% . Determine the approximate value of the vehicle 10 years af
SVEN [57.7K]

Answer:

I believe it is 12,393.86

5 0
3 years ago
PLEASE HELP!!
Rashid [163]

Answer:

The answer is $10.80

Step-by-step explanation:

It goes up $0.70 every mile and the flat fee is $3.10.

The equation 3.1 + 0.7(x) when x is the number of miles traveled.

Substitute 11 for x and get  3.1 + 0.7(11).

The answer is $10.80

5 0
3 years ago
Other questions:
  • A recipe for cookies requires 2/3 cup of butter. Raheim wants to make 3/4 of the recipe. How many cups of butter should Raheim u
    11·2 answers
  • What is the sum 3/5 3/7
    6·1 answer
  • HURRY PLEASE!!
    7·2 answers
  • Б) 3х2 – 10 = 152<br>how to solve with square root​
    8·1 answer
  • A company is evaluating which of two alternatives should be used to produce a product that will sell for $35 per unit. The follo
    6·1 answer
  • Please help Geometry problem
    15·1 answer
  • A teacher recorded the number of days her students went on vacation. Which statements describe the data? Select all that apply.
    14·1 answer
  • Which shows the Commutative Property of Addition?
    12·1 answer
  • Ill mark brainlist plsshelp
    9·1 answer
  • The weights of 5 girls are 70 pounds, 68 pounds, 85 pounds, 62 pounds, and 70 pounds. Nina finds measures of center and measures
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!